Cool Math Vibrations

Feb 25, 2019 | Parker

You hear sounds all day long. Some you probably enjoy (the sound of a shower or bath running) while others you may not (the neighbor’s car alarm that goes off every 20 minutes). Have you ever stopped to think about what sound actually is though? 

Sound is a type of energy made by vibrations. Air particles move when an object vibrates. Air particles bump into other air particles close to them and all of this movement of particles is called sound waves. Sounds waves keep going until the particles run out of energy to bump into one another. If your ear is within range of the vibrations, you hear the sound. Picture throwing a rock into a still swimming pool. The rings of waves expand indefinitely until they hit the edge. The same is true with sound.

Two of the most frequent sounds you probably hear are speech and music. Sound is broken up into a combination of frequencies in speech and music and these frequencies can be calculated by a formula called the Fourier transform, which is named after French mathematician Joseph Fourier. We won’t get technical here, but in this formula, frequencies are broken down into something we call pitch. Pitch is often the word we use to describe a single note or tone that comes from an instrument or human voice. 

Music is often comprised of more simple pitches than speech, specifically when one instrument is played. Instruments such as the piano are singularly sourced pitches without too much vibration. Other instruments like those in the percussion category, produce more complex sounds with a large variance in frequency. You might then hear a variance in pitches from playing just one note on a percussion instrument. When orchestras play, you can combine different pitches together, however, from each individual instrument, the pitch of a note itself doesn’t carry a lot of vibration or complexity.

Speech is a bit more complicated than music, in terms of pitch, because it carries more vibrations in a single note. Also interestingly, speech tends to vary depending on the speaker’s height. The shorter someone is, the higher the pitch of the voice. Children tend to have the highest pitched voices and women come next. Taller men tend to have lower pitched voices versus men who are shorter. 

In addition, the pitches people use when speaking often mean different things in a language. Most of us don’t speak in monotone and in some languages, like Mandarin Chinese, fluctuation of pitch is used to determine the meaning of specific words. There are actually 4 tones in Mandarin that are used in speech. Take the word ma. If you say it the way an English speaker would say it, just reading it from a book say, then it means “scold” in Mandarin. If you were to say ma as if you were looking for your mother, as in ma?, it means “rough.” In other languages, like English, sentences can change based on pitch. Someone who says “The yard?” with a pitch the goes up at the end  is usually asking a question vs. someone who says “The yard.” with the same or lowered pitch at the end.

In US culture, pitch also can mean happiness or menace. Lower ptched voices tend to convey more seriousness and trouble and high pitched voices tend to convey light heartedness and innocence. Two notable high pitched voice examples are that of Alvin from Alvin and the Chipmunks and the voice of Mickey Mouse. They are associated with friendliness and playfulness. Can you think of more examples of famous high and low pitched voices? 

There are several ways to alter the pitch of a voice, like Alvin and Mickey Mouse. The most common way is called pitch shifting, which is sounds recording technique. It’s done using electronic devices that use math to alter pitch, by altering frequencies. All the examples above are done with pitch shifting, along with many more you frequently hear on TV and radio and in movies.

Are you curious what your cartoon voice would sound like, high or low? Audacity is an open-source audio editor that can help you with the basics of pitch shifting your voice into some pretty funny pitches. Have fun and remember, sound, vibrations and pitch can all be explained by math!